If vertices of a parallelogram are respectively $(0, 0)$, $(1, 0)$, $(2, 2)$ and $(1, 2)$, then angle between diagonals is 

The diagonals of a parallelogram $PQRS$ are along the lines $x + 3y = 4$ and $6x - 2y = 7$. Then $PQRS$ must be a

In an isosceles triangle $ABC, \angle C = \angle A$ if point of intersection of bisectors of internal angles $\angle A$ and $\angle C$ divide median of side $AC$ in $3 : 1$ (from vertex $B$ to side $AC$), then value of $cosec \ \frac{B}{2}$ is equal to

A variable straight line passes through a fixed point $(a, b)$ intersecting the co-ordinates axes at $A\,\, \&\,\, B$. If $'O'$ is the origin then the locus of the centroid of the triangle $OAB$ is :

A point starts moving from $(1, 2)$ and its projections on $x$ and $y$ - axes are moving with velocities of $3m/s$ and $2m/s$ respectively. Its locus is

If the coordinates of the points $A,\, B,\, C$ be $(-1, 5),\, (0, 0)$ and $(2, 2)$ respectively and $D$ be the middle point of $BC$, then the equation of the perpendicular drawn from $B$ to the line $AD$ is